Question

A motor boat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of stream.

Answer 1

Given :-

• A motor boat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot.  

To Find :-

• Find the speed of stream.  

Solution :-

As we know that,

★ Speed on upstream = ( Speed of motorboat – Speed of stream )  

★ Speed on downstream = ( Speed of motorboat + Speed of stream )  

★ Time taken = Distance/Speed

• Let the speed of stream be ‘ x km/h ’  

Then,

→ Speed of motorboat on upstream = ( 20 – x ) km/h  

→ Speed of motorboat on downstream = ( 20 + x ) km/h  

Time taken,  

→ To cover 48 km upstream = ( 48/ 20-x ) hours  

→ To cover 48 km downstream = ( 48/ 20+x ) hours  

According to the question :-

$\sf \dashrightarrow \dfrac{48}{20-x} - \dfrac{48}{20+x} = 1$

$\sf \dashrightarrow 48 \{ 20 + x \} - 48 \{ 20 - x \} = \{ 20 -x \} \{ 20 + x \}$

$\sf \dashrightarrow 48 \{ 2x \} = 20^{2} -x^{2}$

$\sf \dashrightarrow 96x = 400 -x^{2}$

$\sf \dashrightarrow 96x +x^{2} = 400$

$\sf \dashrightarrow x^{2} + 96x -400 = 0$

$\sf \dashrightarrow \{ x -4 \} \{ x + 100 \} = 0$

So,  

• x = 4

or  

• x = -100

[ Speed of stream cannot be negative so we’ll take 4 as the speed of stream ]  

Hence,  

• The speed of the stream is 4 km/h

═════════════════════════

Answer 2

A N S W E R :

• Speed of the stream will be 4 km/hours.

Given :

• A motor boat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot

To find :

• Find the speed of stream ?

Solution :

As we know that,

Formula Used :

★ Speed on upstream = D/x - y hrs

★ Speed on downstream = D/x + y hrs

★ Time taken = Distance/Speed

• Let the speed of stream be x km/hrs

Then,

• Speed of boat in upstream is 20 - x

• In downstream, speed of boat is 20 + x

According to the question,

• Time taken in the upstream journey - Time taken in the downstream journey = 1 hrs

=> 48/20 - x - 48/20 + x = 1

=> 20 + x - 20 + x/20² - x² = 1/48

=> 2x/400 - x² = 1/48

=> 2x × 48 = 400 - x²

=> x² + 96x - 400 = 0

=> x² + 100x - 4x - 400 = 0

=> x(x + 100) - 4(x + 100) = 0

=> (x - 4)(x + 100) = 0

=> x = 4 or x = -100

Hence,

• Speed of the stream will be 4 km/hours.